The Catalina range has a few dozen trails (and hundreds of combinations of...) just begging to be used. Elevations start at around 3,000' to 9,000'. If you pick your trails wisely, you might even avoid seeing another human for a couple of days at a time.
The Rincons, on the east side offer the most solitude, and are perfect for backpacking. Rincon Peak and Tanque Verde Peak will usually be busy, but I never seem to see anyone, anywhere else in those mountains.
I've spent over 40 years playing in the mountains around Tucson and would have to say that their diversity can't be beat, and yes, backpacking opportunities abound.
If you need some suggestions, I have have many. Drop me a line.